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1. Introduction The estimation of atmospheric attraction and loading effects are necessary for continuous and precise gravity observations, e.g., with superconducting gravimeters (SG), because gravity variations induced by shifts of air masses cover geodynamic signals of interest. Therefore, this atmospheric impact should be modeled as well as possible and be removed from the gravity observations. A still widely used atmospheric reduction is based upon an admittance factor adjusted by least square fitting between barometric pressure and SG data from an observation site. By using this method, however, only effects which are correlated with local pressure are taken into account and effects uncorrelated are not considered. During the recent past, several attempts were made (e.g. Merriam, 1992; Sun et al. 1995; Boy et al., 1998, 2002; Kroner & Jentsch, 1999; Guo et al., 2004) to improve reductions by means of Green’s functions (Farrell, 1972) or using an empirical frequency-dependent method (Warburton & Goodkind, 1977; Crossley et.al., 1995; Neumeyer, 1995). Merriam (1992) calculated atmospheric Green’s functions (attraction and deformation), which are based on the ideal gas law, the hydrostatic assumption, and a temperature model of the COSPAR (Committee on Space Research) atmosphere. These are computed over a thin column from a height from 0 to 60 km. The attraction and loading effect can be computed from these functions and surface barometric pressure data for the whole Earth. As here only surface pressure is considered, surface pressure independent air mass movements are not taken into account. Neumeyer et al. (2004) computed a physical reduction using three-dimensional (3D) meteorological model data from the European Center for Medium-Range Weather Forecasts (ECMWF). The attraction effect was calculated up to 1.5° distance from the SG station and for the deformation part using Green’s function a distance up to 10° was considered. The amplitude of the attraction part which does not correlate with barometric pressure observed at the Earth’s surface was about 2.0 µGal (Neumeyer et al., 2006). The present investigation is based on the studies by Neumeyer et al. (2004, 2006) and the object of this paper is to derive an optimized atmospheric reduction suitable for ongoing research related to gravity changes of several days and longer (e.g. related polar motion or non-tidal ocean loading etc.). Thus, in this study the focus is atmospheric variations with spatial scales of tens of kilometers to global. Reductions for atmospheric effects are a means to an end, because gravity data interpretation begins after the atmospheric reduction. In this paper, we determine how large the zone needs to be for the computation of the attraction effect using 3D meteorological data and from which distance it is sufficient to use surface data and a standard atmosphere. We use spectral and tidal analyses to investigate and quantify the differences between the various reduction methods. 2. Data and method 2-1 The ECMWF data
7 data sets (surface geopotential, surface pressure, 2 m temperature, humidity with 60/90 height levels, temperature with 60/90 height levels, geopotential with 60/90 height levels, and barometric pressure with 60/90 height levels) from ECMWF Integrated Forecast System (IFS) daily analysis and error estimates are used in this investigation. The original data are re-sampled to a regular grid of 0.5° × 0.5° and the coverage is 89.5° to - 89.5° in latitude and 0° to 359.5° in longitude. The sampling rate is 6 h. Until 31.01.2006, ECMWF provided data for 60 height levels (about up to 64 km height), after this date the number of height levels was increased to 91 (about 80 km height). The gravity effects due to this modification amount to 8.42×10 − 4 µGal in a time span of 11 months. These effects are therefore small enough to be ignored in this study. 2-2 The air density distribution For the estimation of the atmospheric attraction term, the air density distribution needs to be computed for each cell of air mass. The atmosphere is considered as a mixture of dry air and water vapor. By using the ideal gas equation the air density ρ can be derived from p ρ = (1), q RT( 1− q+ ) ε where R is the gas constant for dry air (287.05 Jkg −1 K −1 ), p, q, T are respectively barometric pressure, humidity, temperature taken from ECMWF data (from the Earth’s surface to 80 km height) and ε is the ratio of the gas constants for dry R air R and water vapour R v ( ε = = 0.62197 ) . Fig. 1a shows the air density R v distribution using (1) and ECMWF data for the example of Moxa station (Fig.3)(50.6447° N, 11.6156° E and a height of 455m) for the time span of one month and the vertical density distribution derived from the U.S. Standard Atmosphere 1976 (NASA,1976) and the well-known barometric formula (2) g 0 − P0 ⎛ T0 + αz ⎞ ρ(z)= Rα RT ⎜ Z T ⎟ (2) ⎝ 0 ⎠ with T Z = T 0 + αz and α as the rate of temperature change with height from the US1976 standard atmosphere up to 84 km. P 0 and T 0 are respectively surface pressure and temperature from ECMWF, T Z is temperature at height z, and g 0 is the mean surface gravity value 9.80665 m/s 2 .
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MAREES TERRESTRES BULLETIN D'INFORM
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BIM 146 December 15, 2010 New Chall
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1994), and TPXO.6 (Egbert et al., 1
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4. An attempt to improve the region
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From Fig. 2, we also see that, the
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GPS network called GEONET (GPS Eart
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References Bos, M. S., Baker, T. F.
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Planets Space, 59, 307-311. Sato, T
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Fig. 1. Locations of the observatio
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the dense seismic observation netwo
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difference of loading effects of oc
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is done with an optical lever using
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6. Application of laser interferome
Page 32 and 33: Figure 11. Strain seismograms of th
Page 34 and 35: Higashi, T., 1996, A study on chara
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Page 38 and 39: 2. Fundamentals and techniques At t
Page 40 and 41: 100 low frequencies earth tide freq
Page 42 and 43: Tab. 4: Averages of noise levels at
Page 44 and 45: References Asch, G., Elstner, C., J
Page 46 and 47: The 1 / s part is also worth mentio
Page 48 and 49: As it was mentioned before the resu
Page 50 and 51: Fig. 9. Morlet Wavelet Spectrum, su
Page 52 and 53: 9. CONCLUSIONS This investigation w
Page 54 and 55: 2. Objectives of Aswan Tidal Gravit
Page 56 and 57: 5. Recording of Data The data logge
Page 58 and 59: Figure 5: Pre-processed hourly data
Page 60 and 61: Figure 6: Residuals of gravity tide
Page 64 and 65: time. In addition, models for gravi
Page 66 and 67: Fig. 3 (Zahran, 2005) shows gravity
Page 68 and 69: during the years 2003 and 2004. It
Page 70 and 71: Figure 7: Variation of phase shift,
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Page 78 and 79: 4. Tidal analysis The tidal analysi
Page 80 and 81: References Banka, D., Crossley, D.
Page 84 and 85: Figure 1 Air density distributions
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Page 88 and 89: Figure 4 Attraction effect from the
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Page 96 and 97: Figure 10 SG observation and gravit
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Page 100 and 101: oceans. The effect has a peak-to-pe
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Page 108 and 109: Table 1: Adjusted tidal parameters
Page 110 and 111: Acknowledgements: The authors are i
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